Michael Gove gives good apology. In fact, the education secretary is so accomplished at the apology that he offered two of them, the first to the House of Commons and then again the next day to a local government conference. He chomped through this double serving of humble pie with lashings of grovel sauce after his department bungled the announcement of cuts to the school rebuilding programme.

There's a part of me that finds something quite refreshing about the sight of the politician penitent. They are usually ready to offer regrets only for things that happened centuries ago which were never their responsibility in the first place. Tony Blair once said sorry for the Irish potato famine; Gordon Brown did the same about sending children up chimneys. When it came to their own mistakes, it required the services of a team of crack surgeons working around the clock to extract an apology. In the case of Mr Brown, the operation was even then nearly always a failure.

Michael Gove's readiness to take public responsibility for his department's blundering was a disarming tactic. It is not one, though, that can be employed too often before the apologist becomes ridiculous. Nor has his contrition, while well-judged, drawn all the sting from the anger about his announcement. How could it? He is neither apologising for, nor retreating from, the essential decision. That is to terminate the rebuilding of 700 schools, a cut to a front-line public service about which the voters were not forewarned in the Conservative manifesto.

There's plenty to criticise about the Building Schools for the Future programme bequeathed to the coalition by Labour. Mr Gove blames it for "massive overspends, tragic delays, botched construction projects and needless bureaucracy". He would, wouldn't he? On less partisan accounts, the programme became a consultant-infested monster. Accusations that millions of pounds of public money have been wasted are now likely to be investigated by the public accounts committee, which is chaired by a former Labour minister, Margaret Hodge. But the headline is the headline: schools have been cut.

Labour has gone on the attack, as you'd expect. At some point, when Labour finally has a leader, the opposition will have to come up with a credible explanation for how it would deal with the deficit. For the moment, Labour spokesmen and women are going to say we wouldn't cut like this and we wouldn't cut like that.

The troubles of Michael Gove have been seized on with relish by Ed Balls. There was no loathing lost between the two men when Mr Gove shadowed Mr Balls and, if anything, their mutual antipathy has become even more intense now that the roles are reversed. Mr Balls has been running a highly effective operation to exploit and intensify the furore over the error-riddled list of cancelled school building projects. He is a man who likes to have his teeth in an opponent's jugular and has enjoyed drawing some first blood from the coalition. It displays to the selectorate of the Labour party his best claim to be their next leader. If Labour wants to be led by a pleasant-looking, thoughtful kind of guy who can make a pretty speech and turn a fancy phrase, it will plump for one of the Miliband boys. If Labour wants a leader who is a killing machine, Mr Balls has been gifted the chance to show his party that he is their man.

Liberal Democrats have been voicing discontent. The leader of their group on Liverpool council says the decision has made him "physically sick". Anguish and anger from them was to be expected as well. It fits into the general media narrative that the fault line in the coalition is between agonised, cuts-shy, squishy Liberals and ruthless, flinty, slashing Tories. But there is uproar among some Conservatives, too, which tells us that the chemistry of this government is much more complicated than a simple division between hand-wringing Libs and heartless Tories.

Some Lib Dem ministers have been comradely towards the education secretary, even sending him messages of sympathy and support. It is backbenchers of Michael Gove's own party who have been sounding off most furiously. Iain Liddell-Grainger, the Conservative MP for Bridgwater, is hopping mad that three schools in his constituency have been halted and another three have been put under review. He has even threatened to lead parents and children on a protest march to Westminster. Perhaps the Conservative MP should have some T-shirts and placards printed with the slogan: "No to Tory cuts".

Philip Davies, another Tory MP furious about cancelled school building projects in his Yorkshire constituency of Shipley, is planning to challenge the education secretary when he faces the Commons tomorrow. These are not MPs known as wet types of Tories. They are both men of the right. More career-minded Conservatives are keeping their discontent private, but they are just as cross. One new, young, bright, Cameroonian Tory MP despairs: "Why didn't we present this as a review of capital projects? It makes it look like we are axeing schools." Well, yes, it does look that way, perhaps because they are axeing schools.

This eruption around a cabinet minister who is part of the Cameron inner circle should send a big warning to the government. Their honeymoon with most of the media, which has helped to create a fairly positive mood towards the coalition among most voters, had started to induce complacency. Senior figures at both Number 10 and the Treasury were amazed and relieved that George Osborne's budget, the most draconian combination of tax rises and spending cuts introduced by any government since 1945, was not greeted with more hostility. That was mainly, I suspect, because its effects are still theoretical to most people. The increase to VAT and other tax rises have yet to hit disposable incomes. The public can hear the spending axe swishing through the air, but it has not bitten much flesh yet.

Emboldened by the false sense of security which has come from the deceptively benign reaction to the budget, the government's rhetoric on cuts has begun to sound near gleeful about the ferocity of the spending squeeze. They have started to appear not regretful, but boastful that they are planning the deepest and swiftest cuts in modern British history. At the time of the budget, it was being suggested that the non-ringfenced departments faced real reductions in spending of 25%. That was eye-watering enough. Some senior officials think it will prove impossible. No British government of the modern era has come close to reducing spending on that scale at this speed.

The braggadocio about cuts has alarmed even the likes of John Redwood, who warns: "Ministers would be wise to tone down the rhetoric of massive cuts." David Cameron is becoming nervous that the government is leaving the public and the media with the impression that cutting is the sole, defining purpose of the coalition. He said in a speech on Thursday: "People are making a big mistake if they think this government is just about sorting out the deficit."

People have been encouraged to think that by his own ministers, especially the noises about cuts emanating from the Treasury. Last weekend, it was being bruited that some departments, including the Home Office and transport, were being asked by the Treasury to identify spending reductions of up to 40%. That is a figure which is incredible in every sense of the word.

The furore around Michael Gove ought to serve as a caution to his colleagues. It illustrates how easy it is to swagger your machismo as an axeman when you are talking abstract percentages and how hard it is when you have to bring down the blade. It is one thing to type some numbers into a Whitehall spreadsheet and quite another to translate them into real cuts to real services used by real voters.

The reductions to the school building programme amount to a saving of only £1bn a year. I say only because, while that sounds like a big sum to anyone who is not Bill Gates, it is a microscopic fraction of the global total of cuts planned by the coalition. I am sure there will be lots of incandescent parents, heads and teachers, especially among those who were initially told their school building project was going ahead, only to find that it had been axed. I hope they will understand why I observe that they represent a minuscule fraction of the population.

This relatively tiny cut impacting on a very small proportion of the public has handed ammunition to the opposition, aroused much agitation on the government's own side, and forced two apologies from one of the key members of the cabinet. You do not need much imagination to see the opposition that will confront the coalition when they start to implement the big cuts which will impact on large numbers of voters.

The turbulence around the education secretary is but a light squall compared to the dark tornadoes of trouble coming over the horizon.